Introduction to Network Inference in Genomics

  • Ernst C. WitEmail author


The genome is the archetypical complex system: it is a finely tuned whole whose many parts, such as DNA, RNA and proteins, interact at various levels to execute intricate functions, such as repair, replication and adapting to the external environment. One particularly effective way of conceptualizing this complex system is by means of a network, in which the vertices describe the genomic components and the edges describe their physical or functional interactions. With the advent of modern high-throughput genomic measuring devices, such as microarrays, RNA-seq and other next generation sequencing tools, it has become possible to measure the vertices of the genomic system in real time. One central question is whether from these measurements it is possible to reconstruct the edges of the genomic network. This essay describes three modelling and inference strategies to answer this central biological question.


  1. Abegaz, F. & Wit, E. (2013), ‘Sparse time series chain graphical models for reconstructing genetic networks’, Biostatistics14(3), 586–599.CrossRefGoogle Scholar
  2. Aderhold, A., Husmeier, D. & Grzegorczyk, M. (2014), ‘Statistical inference of regulatory networks for circadian regulation’, Statistical applications in genetics and molecular biology13(3), 227–273.MathSciNetCrossRefGoogle Scholar
  3. Akutsu, T., Miyano, S. & Kuhara, S. (1999), ‘Identification of genetic networks from a small number of gene expression patterns under the \(\text{Boolean}\) network model’, Pacific Symposium on Biocomputing pp. 17–28.Google Scholar
  4. Behrouzi, P. & Wit, E. C. (2017), ‘Detecting epistatic selection with partially observed genotype data by using copula graphical models’, Journal of the Royal Statistical Society: Series C (Applied Statistics).Google Scholar
  5. Bellman, R. & Roth, R. S. (1971), ‘The use of splines with unknown end points in the identification of systems’, Journal of Mathematical Analysis and Applications34(1), 26–33.MathSciNetCrossRefGoogle Scholar
  6. Bower, J. M. & Bolouri, H. (2001), Computational Modelling of Genetic and Biochemical Networks, 2nd edn, Massachusetts Institute of Technology.Google Scholar
  7. Brunel, N. J-B (2008), ‘Parameter estimation of ODE’s via nonparametric estimators’, Electronic Journal of Statistics2, 1242–1267.MathSciNetCrossRefGoogle Scholar
  8. Carlin, B. P. & Louis, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis, 2nd edn, Chapman and Hall/CRC.Google Scholar
  9. Corominas, R., Yang, X., Lin, G. N., Kang, S., Shen, Y., Ghamsari, L., Broly, M., Rodriguez, M., Tam, S., Trigg, S. A. et al. (2014) , ‘Protein interaction network of alternatively spliced isoforms from brain links genetic risk factors for autism’, Nature communications5.Google Scholar
  10. Costanzo, M., VanderSluis, B., Koch, E. N., Baryshnikova, A., Pons, C., Tan, G., Wang, W., Usaj, M., Hanchard, J., Lee, S. D. et al. (2016), ‘A global genetic interaction network maps a wiring diagram of cellular function’, Science353(6306), aaf1420.Google Scholar
  11. Dahlhaus, R. & Eichler, M. (2003), Causality and graphical models in time series analysis, in R. S., ed., ‘Highly Structured Stochastic Systems’, Oxford University Press, pp. 115–137.Google Scholar
  12. Dattner, I. & Klaassen, C. A. (2013), ‘Estimation in systems of ordinary differential equations linear in the parameters’, arXiv:1305.4126 .
  13. Downward, J. (2003), ‘Targeting RAS signalling pathways in cancer therapy’, Nature Reviews Cancer3(1), 11.CrossRefGoogle Scholar
  14. Eraker, B. (2001), ‘\({MCMC}\) analysis of diffusion models with application to finance’, Journal of Business and Economic Statistics19(2), 177–191.MathSciNetCrossRefGoogle Scholar
  15. Érdi, P. & Tóth, J. (1989), Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester University Press.Google Scholar
  16. Fang, Y., Wu, H. & Zhu, L.-X. (2011), ‘A two-stage estimation method for random coefficient differential equation models with application to longitudinal HIV dynamic data’, Statistica Sinica21(3), 1145–1170.MathSciNetCrossRefGoogle Scholar
  17. Gawad, C., Koh, W. & Quake, S. R. (2016), ‘Single-cell genome sequencing: current state of the science’, Nature reviews. Genetics17(3), 175.CrossRefGoogle Scholar
  18. Gillespie, D. (1992), Markov processes: An introduction for physical scientists., Academic Press.Google Scholar
  19. Gillespie, D. T. (1996), ‘The multivariate Langevin and Fokker-Planck equations’, American Journal of Physics64(10), 1246–1257.MathSciNetCrossRefGoogle Scholar
  20. Golightly, A. & Wilkinson, D. J. (2005), ‘Bayesian inference for stochastic kinetic models using a diffusion approximation’, Biometrics61(3), 781–788.MathSciNetCrossRefGoogle Scholar
  21. Golightly, A. & Wilkinson, D. J. (2008), ‘Bayesian inference for nonlinear multivariate diffusion models observed with error’, Computational Statistics and Data Analysis52(3), 1674–1693.MathSciNetCrossRefGoogle Scholar
  22. González, J., Vujačić, I. & Wit, E. (2013), ‘Inferring latent gene regulatory network kinetics’, Statistical applications in genetics and molecular biology12(1), 109–127.MathSciNetCrossRefGoogle Scholar
  23. González, J., Vujačić, I. & Wit, E. (2014), ‘Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations’, Pattern Recognition Letters45, 26–32.CrossRefGoogle Scholar
  24. Granger, C. W. (1988), ‘Causality, cointegration, and control’, Journal of Economic Dynamics and Control12(2-3), 551–559.CrossRefGoogle Scholar
  25. Grzegorczyk, M. & Husmeier, D. (2011), ‘Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes’, Bioinformatics27(5), 693–699.CrossRefGoogle Scholar
  26. Grzegorczyk, M., Husmeier, D., Edwards, K. D., Ghazal, P. & Millar, A. J. (2008), ‘Modelling non-stationary gene regulatory processes with a non-homogeneous Bayesian network and the allocation sampler’, Bioinformatics24(18), 2071–2078.CrossRefGoogle Scholar
  27. Gugushvili, S. & Klaassen, C. A. J. (2012), ‘\(\sqrt{n}\)-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing’, Bernoulli18, 1061–1098.MathSciNetCrossRefGoogle Scholar
  28. Gugushvili, S. & Spreij, P. (2012), ‘Parametric inference for stochastic differential equations: a smooth and match approach’, ALEA9(2), 609–635.MathSciNetzbMATHGoogle Scholar
  29. Hilger, R., Scheulen, M. & Strumberg, D. (2002), ‘The Ras-Raf-MEK-ERK pathway in the treatment of cancer’, Oncology Research and Treatment25(6), 511–518.CrossRefGoogle Scholar
  30. Hooker, G., Ellner, S., Earn, D. et al. (2011), ‘Parameterizing state-space models for infectious disease dynamics by generalized profiling: measles in ontario.’, Journal of the Royal Society, Interface8(60), 961–974.Google Scholar
  31. Hornberg, J. J. (2005), Towards integrative tumor cell biology control of \(\text{ MAP }\) kinase signalling, PhD thesis, Vrije Universiteit, Amsterdam.Google Scholar
  32. Liang, H. & Wu, H. (2008), ‘Parameter estimation for differential equation models using a framework of measurement error in regression models’, Journal of the American Statistical Association103(484), 1570–1583.MathSciNetCrossRefGoogle Scholar
  33. Macaulay, I. C., Ponting, C. P. & Voet, T. (2017), ‘Single-cell multiomics: multiple measurements from single cells’, Trends in Genetics.Google Scholar
  34. Michaelis, L. & Menten, M. L. (1913), ‘The kinetics of the inversion effect’, Biochem. Z49, 333–369.Google Scholar
  35. Moyal, J. (1949), ‘Stochastic processes and statistical physics.’, Journal of the Royal Statistical Society. Series B11, 150–210.Google Scholar
  36. Papoutsakis, E. T. (1984), ‘Equations and calculations for fermentations of butyric acid bacteria’, Biotechnology and bioengineering26(2), 174–187.CrossRefGoogle Scholar
  37. Purutçuoğlu, V. & Wit, E. (2008), ‘Bayesian inference for the MAPK/ERK pathway by considering the dependency of the kinetic parameters’, Bayesian Analysis3(4), 851–886.MathSciNetCrossRefGoogle Scholar
  38. Qi, X. & Zhao, H. (2010), ‘Asymptotic efficiency and finite-sample properties of the generalized profiling estimation of parameters in ordinary differential equations’, The Annals of Statistics38(1), 435–481.MathSciNetCrossRefGoogle Scholar
  39. Ramsay, J. O., Hooker, G., Campbell, D. & Cao, J. (2007), ‘Parameter estimation for differential equations: a generalized smoothing approach’, Journal of the Royal Statistical Society: Series B (Statistical Methodology)69(5), 741–796.MathSciNetCrossRefGoogle Scholar
  40. Risken, H. (1984), The Fokker-Planck Equation: Methods of Solution and Applications, Springer-Verlag.Google Scholar
  41. Roberts, G. O. & Stramer, O. (2001), ‘On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm’, Biometrika88(3), 603–621.MathSciNetCrossRefGoogle Scholar
  42. Schwartzman, O. & Tanay, A. (2015), ‘Single-cell epigenomics: techniques and emerging applications’, Nature reviews. Genetics16(12), 716.CrossRefGoogle Scholar
  43. Sotiropoulos, V. & Kaznessis, Y. (2011), ‘Analytical derivation of moment equations in stochastic chemical kinetics.’, Chemical engineering science66(3), 268–277.Google Scholar
  44. Stegle, O., Teichmann, S. A. & Marioni, J. C. (2015), ‘Computational and analytical challenges in single-cell transcriptomics’, Nature reviews. Genetics16(3), 133.CrossRefGoogle Scholar
  45. Stein, T., Morris, J. S., Davies, C. R., Weber-Hall, S. J., Duffy, M.-A., Heath, V. J., Bell, A. K., Ferrier, R. K., Sandilands, G. P. & Gusterson, B. A. (2004), ‘Involution of the mouse mammary gland is associated with an immune cascade and an acute-phase response, involving lbp, cd14 and stat3’, Breast Cancer Res6, R75–R91.Google Scholar
  46. Steinke, F. & Schölkopf, B. (2008), ‘Kernels, regularization and differential equations’, Pattern Recognition41(11), 3271–3286.CrossRefGoogle Scholar
  47. Tibshirani, R. (1996), ‘Regression shrinkage and selection via the lasso’, Journal of the Royal Statistical Society. Series B (Methodological) pp. 267–288.Google Scholar
  48. Van Kampen, N. G. (1981), Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam.zbMATHGoogle Scholar
  49. Varah, J. (1982), ‘A spline least squares method for numerical parameter estimation in differential equations’, SIAM Journal on Scientific and Statistical Computing3(1), 28–46.MathSciNetCrossRefGoogle Scholar
  50. Vinciotti, V., Augugliaro, L., Abbruzzo, A. & Wit, E. C. (2016), ‘Model selection for factorial Gaussian graphical models with an application to dynamic regulatory networks’, Statistical applications in genetics and molecular biology15(3), 193–212.MathSciNetCrossRefGoogle Scholar
  51. Vujačić, I., Dattner, I., González, J. & Wit, E. (2015), ‘Time-course window estimator for ordinary differential equations linear in the parameters’, Statistics and Computing25(6), 1057–1070.MathSciNetCrossRefGoogle Scholar
  52. Vujačić, I., Mahmoudi, S. M. & Wit, E. (2016), ‘Generalized Tikhonov regularization in estimation of ordinary differential equations models’, Stat5(1), 132–143.MathSciNetCrossRefGoogle Scholar
  53. Wilkinson, D. J. (2006), Stochastic Modelling for Systems Biology, Chapman and Hall/CRC.Google Scholar
  54. Wit, E., Heuvel, E. v. d. & Romeijn, J.-W. (2012), “All models are wrong...’: an introduction to model uncertainty’, Statistica Neerlandica66(3), 217–236.Google Scholar
  55. Wu, M. & Singh, A. K. (2012), ‘Single-cell protein analysis’, Current Opinion in Biotechnology23(1), 83–88.CrossRefGoogle Scholar
  56. Xun, X., Cao, J., Mallick, B., Maity, A. & Carroll, R. J. (2013), ‘Parameter estimation of partial differential equation models’, Journal of the American Statistical Association108(503), 1009–1020.MathSciNetCrossRefGoogle Scholar
  57. Yin, J. & Li, H. (2011), ‘A sparse conditional Gaussian graphical model for analysis of genetical genomics data’, The Annals of Applied Statistics5(4), 2630.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Computational ScienceUniversità Della Svizzera ItalianaLuganoSwitzerland

Personalised recommendations